Forecasting nuclear proliferation/GDPs of nuclear-weapon states

The statistical computations behind the figure giving "Gross Domestic Product (GDP) of nuclear-weapon states" in the Wikiversity article on "Forecasting nuclear proliferation" can be replicated by "knitting" the R Markdown code in this vignette in Rstudio.

RStudio RMarkdown knit icon

Process

Gross Domestic Product (GDP) of nuclear-weapon states in billions of 2019 US dollars at Purchasing Power Parity (PPP) before (dashed line), during (thick solid line) and after (thinner solid line) their nuclear-weapons program leading to their first test of a nuclear weapon. (Country codes as with Figure 1.) The dotted line indicates the total cost of the Manhattan Project that developed the very first nuclear weapon from 1942 to the end of 1945.

1. Open an instance of RStudio. If you don't already have it installed, you can go to "RStudio Cloud" and click "get started for free" (at least as of 2020-10-24). Or you can download and install free and open-source versions of it and R on your local computer. R is available from The Comprehensive R Archive Network. For RStudio, go to its webside > Products (top center) > RStudio > "RStudio Desktop" > "Open Source Edition" > "Download RStudio Desktop".
2. Start RStudio. Then File > "New File" > "R Markdown..." > Title: "GDPs of nuclear-weapon states" > PDF > OK.
3. Replace the default code in this new RMarkdown vignette on "GDPs of nuclear-weapon states" with the text from the section below entitled, 'RMarkdown vignette on "GDPs of nuclear-weapon states"'.
4. Save.
5. File > "New File" > "Text File".
6. Copy the text from the section below entitled "GDP-references.bib" into this new empty text file.
7. Save as "GDP-references.bib".
8. Click the "Knit" icon; see the companion image. Or read the text and run the code chunks one at a time manually. The latter makes it relatively easy to look at intermediate computations carefully and experiment with changing things in different ways.

Development of this vignette

This vignette was developed when it was decided that this article could benefit from the financial analysis in the accompanying plot of the GDPs of nuclear-weapon states before, during and after their their nuclear-weapons programs. This became "Figure 2" in "Forecasting nuclear proliferation".

RMarkdown vignette on "Gross Domestic Products (GDPs) of nuclear-weapon states"

---
title: "GDPs of nuclear-weapon states"
author: "Spencer Graves"
date: "7/3/2020"
#output: html_document
output: bookdown::pdf_book
bibliography: GDP-references.bib
vignette: >
  %\VignetteIndexEntry{GDP of nuclear-weapon states}
  %\VignetteKeyword{GDP}
  %\VignetteKeyword{nuclear-weapon states}
  %\VignetteEngine{knitr::knitr}
  %\SweaveUTF8
  \usepackage[utf8](inputenc)
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Intro 

It's fairly expensive to develop nuclear weapons.  This cost can be divided into two parts:
<ol>
<li class="one">The cost of acquiring the knowledge of how to make nuclear weapons given access to the necessary fissile materials.</li>
<li class="two">The cost of acquiring the necessary fissile materials.</li>
</ol>

For the first part, the costs have declined over time with advances in understanding of nuclear physics including increased dissemination of the knowledge of how to work with these very dangerous materials.    

The cost of acquiring the necessary fissile materials have experienced changes, some of which have increased the costs while others have decreased them.  As more countries and more people have acquired access to fissile material, that has made it easier for people desiring such materials to acquire them.  

However, over time, more people have become more aware of the dangers of nuclear proliferation.  This had led to more restrictions on transfers of fissile materials and "dual use" technologies that can be used to refine the fissile materials and get them into desired levels of purity and physical shape.  

In this article we consider the gross domestic projects of the existing nuclear weapon states and how they compare with the reported cost of the [Manhattan Project](https://en.wikipedia.org/wiki/Manhattan_Project#Cost).  

# Maddison Project Data 

We begin by reading the [Gross Domestic Product (GDP)](https://en.wikipedia.org/wiki/Gross_domestic_product) data from the [Maddison Project](https://en.wikipedia.org/wiki/Maddison_Project).  

```{r findData}
(MaddisonFile <- dir(pattern='8\\.xlsx$'))

gotDat <- (length(MaddisonFile)==1)

if(gotDat){
  library(openxlsx)
  str(Maddison <- read.xlsx(MaddisonFile, 
                      sheet='Full data'))
}
```

# `nuclearWeaponStates` 

To use this, we need the country codes for the existing nuclear-weapon states.  

```{r ctries}
library(Ecdat)
str(nuclearWeaponStates)
```

# Cost of Manhattan Project 

[Hewlett and Anderson (1962) estimated that the total cost of the Manhattan Project through December 31, 1945, was $1.89 billion in current dollars.](https://www.governmentattic.org/5docs/TheNewWorld1939-1946.pdf)^[Hewlett:1962, p. 723 (787/831 in the pdf).]

```{r cost1945}
ManhattanCost1945 <- 1.89e9
```

# Deflators 

We will adjust this number and the Maddison data to billions of 2019 US dollars using GDP Deflators (index 2012=100) from [Measuring Worth](https://www.measuringworth.com/datasets/usgdp/result.php).^[@Williamson:2020.]  

```{r deflators}
deflators <- c("1945"=9.79, "2011"=98.12, "2019"=112.35)

(ManhattanCost2019 <- 
  (ManhattanCost1945 * deflators["2019"]
            / (deflators["1945"] * 1e9) ))
```

# GDP in 2019 dollars 

The Maddison project data includes `pop` = population estimates in thousands and two different estimates of gross domestic product (GDP) per capita in 2011 US dollars:  
1.  `cgdppc` = GDP per capita estimated to support comparisons between in purchasing power parity.  
2.  `rgdpnapc` = GDP per capita estimated to support comparisons in the rates of economic growth between countries, again in purchasing power parity.  

We will use the first to compute GDP in millions of 2019 US dollars.    

```{r MaddisonGDP }
if(gotDat){
  Maddison$GDP <- with(Maddison, 
        pop*cgdppc*deflators["2019"]
        / (deflators["2011"]*1e6) ) 
}
```

# Plot GDPs 

We want to plot the GDPs of the current nuclear-weapon states since the first country made a substantive commitment to develop them, `r min(nuclearWeaponStates$startNucPgm)`.  We'll plot:

* different colors for each country, 

* different textures before, during, and after their `firstTest`, and 

* vary the line width, thinnest before and thickest during the preparations for their `firstTest`.

```{r plotGDPs}
# first establish the scales
nNucStates <- nrow(nuclearWeaponStates)
GDPrng <- matrix(NA, nNucStates, 2)
rownames(GDPrng) <- nuclearWeaponStates$ctry
colnames(GDPrng) <- c('min', 'max')

yrRng <- GDPrng
labelLines <- GDPrng
colnames(labelLines) <- c('year', 'offset')

if(gotDat){
  for(i in 1:nNucStates){
    seli <- (Maddison$countrycode==
             nuclearWeaponStates$Maddison[i])
    sely <- (floor(nuclearWeaponStates[i, 
              "startNucPgmYr"]) <= Maddison$year)
    selyi <- (seli & sely)
    yrRng[i, ] <- range(Maddison[selyi, "year"])
    GDPrng[i, ] <- range(Maddison[selyi, "GDP"], 
                       na.rm=TRUE)
  }

  xrng <- range(yrRng)
  yrng <- range(GDPrng)

  ttl <- paste('GDPs of nuclear-weapon states', 
      '(billions of 2019 USD)', sep='\n')

  sely1 <- (floor(nuclearWeaponStates[i, 
             "startNucPgmYr"]) <= Maddison$year)

# Where to label the lines:  
# year and offset (multiple of GDP for that year)
  adj2 <- 1.5
  adj.5 <- 2/3
  labelLines['US', ] <- c(1943, adj2)
  labelLines['RU', ] <- c(1946, 1.8)
  labelLines['GB', ] <- c(1948, .78)
  labelLines['FR', ] <- c(1960, adj.5)
  labelLines['CN', ] <- c(1964, adj2)
  labelLines['IN', ] <- c(1974, adj.5)
  labelLines['IL', ] <- c(1979, adj2)
  labelLines['PK', ] <- c(1998, adj2)
  labelLines['KP', ] <- c(2006, adj2)

  plotGDPs <- function(Main=ttl, 
           lwd. = c(1, 2, 4), ...){
    plot(xrng, yrng, log='y', type='n', 
       ylab='', las=1, xlab='', main=Main)

    for(i in 1:nNucStates){
      seli <- (Maddison$countrycode==
             nuclearWeaponStates$Maddison[i])
# dashed line before 
#      selyi1 <- (seli & sely1)
#      lines(GDP~year, Maddison[selyi1, ], 
#          lty=2, lwd=lwd.[1], col=i)
      lines(GDP~year, Maddison[seli, ], 
          lty=2, lwd=lwd.[1], col=i)
# solid line since start 
      sely <- (floor(nuclearWeaponStates[i, 
              "startNucPgmYr"]) <= Maddison$year)
      selyi <- (seli & sely)
      lines(GDP~year, Maddison[selyi, ], 
          lwd=lwd.[2], col=i)
# wider line during initial development 
      selend <- (Maddison$year <= 
        ceiling(nuclearWeaponStates[i, 'firstTestYr']))
      selind <- (selyi & selend)
      lines(GDP~year, Maddison[selind, ], 
          lwd=lwd.[3], col=i)
# Label the lines 
      selLblYr <- (Maddison$year == labelLines[i, 1])
      selLbli <- (seli & selLblYr)
      text(labelLines[i, 1], 
         labelLines[i, 2] * Maddison$GDP[selLbli], 
         nuclearWeaponStates$ctry[i], 
         col=i)
    }
# Cost of the Manhattan project 
    abline(h=ManhattanCost2019, lty=3)
# Label the Manhattan project 
    text(1995, ManhattanCost2019*.75, 
       'Manhattan Project')
  }

  plotGDPs()
}
```

Write this to an `svg`s file without the title for Wikimedia Commons.  

```{r svg}
if(gotDat){
  svg('NucWeaponStatesGDP.svg')
  par(mar=c(5, 4, 2, 2)+.1, cex=1.4)
  plotGDPs('', c(2, 4, 8))
  dev.off()
}
```

Create a `png` version also.  

```{r png}
if(gotDat){
  png('NucWeaponStatesGDP.png', 
      width=960, height=960)
#par(mar=c(5, 4, 2, 2)+.1, cex=3, cex.axis=1.1)
  par(mar=c(4, 3, 1, 1)+.1, cex=3.3, cex.axis=.8)
  plotGDPs('', c(2, 4, 8))
  dev.off()
}
```

# References

GDP-references.bib

@Article{Bolton:2012, 
  author={Derek Bolton}, 
  title = {North Korea’s Nuclear Program}, 
  url = {https://www.americansecurityproject.org/ASP%20Reports/Ref%200072%20-%20North%20Korea%E2%80%99s%20Nuclear%20Program%20.pdf}, 
  date = {2012-08}, 
  publisher = {American Security Program}, 
  urldate = {2020-07-15}, 
}

@Book{Hewlett:1962, 
  author={Richard G. Hewlett and Oscar E. Anderson, Jr.}, 
  title = {The New World, 1939/1946, A History of The United States Atomic Energy Commission, Volume I}, 
  publisher={Pennsylvania State University Press}, 
  year = {1962}, 
  url = {https://www.governmentattic.org/5docs/TheNewWorld1939-1946.pdf}, 
  urldate = {2020-07-15}
}

@Book{Nichols:1987, 
  author={Kenneth David Nichols}, 
  title = {The Road to Trinity: A Personal Account of How America's Nuclear Policies Were Made}, 
  publisher={William Morrow and Company}, 
  year = {1987}
}

@Online{Williamson:2020, 
  author = {Samuel H. Williamson}, 
  title={What Was the U.S. GDP Then?}, 
  publisher = {MeasuringWorth}, 
  year = {2020}, 
  url={https://www.measuringworth.com/datasets/usgdp/result.php}, 
  urldate={2020-06-07}
}